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Quantum State Reconstruction of a Bose-Einstein Condensate

Mancini, S, Tombesi, P

Published Jan 1, 1997• 10 citations
OpenAlex

Abstract

We propose a tomographic scheme to reconstruct the quantum state of a Bose-Einstein condensate, exploiting the radiation field as a probe and considering the atomic internal degrees of freedom. The density matrix in the number state basis can be directly retrieved from the atom counting probabilities.

Related papers

Quantum state reconstruction of a Bose-Einstein condensate

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We propose a tomographic scheme to reconstruct the quantum state of a Bose-Einstein condensate, exploiting the radiation field as a probe and considering the atomic internal degrees of freedom. The density matrix in the number state basis can be directly retrieved from the atom counting probabilities.

arXiv:quant-ph/9710038•Europhysics Letters (EPL)•Nov 15, 1997•16 citations

Toward a tomographic picture of a Bose–Einstein condensate

Stefano Mancini, Mauro Fortunato, Paolo Tombesi +1 more

The possibilities of applying tomographic techniques to a Bose-Einstein condensate to reconstruct its ground state are investigated by means of numerical simulations. Two situations for which the density-matrix elements can be retrieved from atom counting probabilities are considered. The methods presented here allow one to distinguish among various possible quantum states.

arXiv:quant-ph/0106089•Journal of the Optical Society of America A•Dec 1, 2000•7 citations

Reconstruction of the Joint State of a Two-Mode Bose-Einstein Condensate

Eric L. Bolda, Sze Meng Tan, Daniel F. Walls

We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.

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Tomographic reconstruction of quantum correlations in excited Bose-Einstein condensates

Anders S. Mouritzen, Klaus Mølmer

We propose to use quantum tomography to characterize the state of a perturbed Bose-Einstein condensate. We assume knowledge of the number of particles in the zero-wave-number mode and of density distributions in space at different times, and we treat the condensate in the Bogoliubov approximation. For states that can be treated with the Gross-Pitaevskii equation, we find that the reconstructed density operator gives excellent predictions of the second moments of the atomic creation and annihilation operators, including the one-body density matrix. Additional inclusion of the momentum distribution at one point of time enables somewhat reliable predictions to be made for the second moments for mixed states, making it possible to distinguish between coherent and thermal perturbations of the condensate. Finally, we find that with the observation of the zero-wave-number mode anomalous second moment $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}^{\ifmmode\dagger\else\textdagger\fi{}}⟩$, the reconstructed density operator gives reliable predictions of the second moments of locally amplitude squeezed states.

arXiv:cond-mat/0409500•Physical Review A•Mar 2, 2005•4 citations

Measuring the multiparticle state of a two-mode Bose-Einstein condensate

Eric L. Bolda, S. M. Tan, Daniel F. Walls

Summary form only given. Much recent interest in the new dilute alkali Bose-Einstein condensate sytems from the idea that the multiparticle state may be highly squeezed due to collisions. The internal states of the atoms can serve as a probe of this squeezing. Motivated by the success of homodyne tomography in measuring the quantum state of light, we propose to obtain the complete density matrix of a two-mode condensate from repeated atom-counting measurements.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations

Transferring the atom statistics of a Bose-Einstein condensate to an optical field

Christopher P. Search, P. R. Berman

We consider a single-mode Bose-Einstein condensate with an arbitrary initial density matrix. This mode is coupled to another condensate mode via a quantized optical-field. We describe a method for transferring the diagonal elements of the initial density matrix in a number state basis to the optical-field's density matrix.

Physical Review A•Sep 12, 2001•7 citations
We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.
We propose to use quantum tomography to characterize the state of a perturbed Bose-Einstein condensate. We assume knowledge of the number of particles in the zero-wave-number mode and of density distributions in space at different times, and we treat the condensate in the Bogoliubov approximation. For states that can be treated with the Gross-Pitaevskii equation, we find that the reconstructed density operator gives excellent predictions of the second moments of the atomic creation and annihilation operators, including the one-body density matrix. Additional inclusion of the momentum distribution at one point of time enables somewhat reliable predictions to be made for the second moments for mixed states, making it possible to distinguish between coherent and thermal perturbations of the condensate. Finally, we find that with the observation of the zero-wave-number mode anomalous second moment $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{0}^{\ifmmode\dagger\else\textdagger\fi{}}⟩$, the reconstructed density operator gives reliable predictions of the second moments of locally amplitude squeezed states.